Finite Group Databasebeta

← #28389263

Subgroups — #28389263

Order 14464.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299153C211yesmaximal, characteristic
2#20298620C211yesmaximal, characteristic
3C4⋊C8×D113C211yesmaximal, characteristic
4#20298346C211yesmaximal, characteristic, complemented
5#20298346C211yesmaximal, characteristic, complemented
6#20298344C211yesmaximal, characteristic, complemented
7#332×C113C211yesmaximal, characteristic, complemented
8C2×#14268630—21no—
9C2×C8×D113—21no—
10#16813622C2211yescharacteristic
11#16813613—21no—
12#16813602C412yes—
13#16813598—21no—
14Q8×Dic113—21no—
15#16813587C412yes—
16#16813580—21no—
17C42×D113C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19C4⋊#11744751C2211yescharacteristic
20#16813551—21no—
21#16813551—21no—
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25C2×Dic226C2×C412yes—
26C2×C4×D113C2×C411yescharacteristic
27C2×C4×D113D411yescharacteristic
28C2×C4×D113D411yescharacteristic
29#14268630—42no—
30C2×#11744751—21no—
31C2×#11744751—21no—
32C8×D113—42no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—22no—
36#14268626—22no—
37#14268624—22no—
38C4×Dic113—22no—
39C4×Dic113C2×C411yescharacteristic
40C4×Dic113D411yescharacteristic
41C4×Dic113D411yescharacteristic
42C2×Q8×C113—21no—
43C2×C8×C113—21no—
44C2×C8×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113C2×C412yes—
47C42×C113C2311yescharacteristic
48C22×D113C22⋊C411yescharacteristic
49Q8×C113—41no—
50Q8×C113—41no—
51C2×C4×C113—22no—
52C2×C4×C113C22×C411yescharacteristic
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×Dic113—22no—
56C2×Dic113C22⋊C411yescharacteristic
57C2×Dic113C22⋊C411yescharacteristic
58C2×Dic113C22⋊C411yescharacteristic
59C4×D113—21no—
60C4×D113—21no—
61C4×D113—41no—
62C4×D113SD1612yes—
63C4×D113Q1612yes—
64Dic226—42no—
65C8×C113—41no—
66C8×C113—41no—
67#11744751—41no—
68#11744751—41no—
69C22×C113C2×C22⋊C411yescharacteristic
70C2×D113—21no—
71C2×D113—21no—
72C2×D113#10312yes—
73C4×C113—21no—
74C4×C113—42no—
75C4×C113C2×SD1611yescharacteristic
76C4×C113C2×Q1611yescharacteristic
77C4×C113AGL(1,ℤ/8)11yescharacteristic
78C4×C113#13711yescharacteristic
79Dic113—21no—
80Dic113—21no—
81Dic113—42no—
82Dic113#10312yes—
83C2×C113#41311yescharacteristic
84C2×C113C2×#10311yescharacteristic
85C2×C113#41711yescharacteristic
86D113—22no—
87#1550—1131nomaximal, Sylow
88C113#155011yescharacteristic, complemented, Sylow
89#533—1131no—
90#423—1131no—
91C2×C4⋊C8—1131no—
92#333—1131no—
93#333—1131no—
94#332—1131no—
95#332D11311yescharacteristic, complemented
96C2×M16—2261no—
97C22×C8—2261no—
98C4⋊Q8—1131no—
99C4⋊Q8C2×D11311yescharacteristic
100#125—2261no—
101C22⋊Q8—1132no—
102C22⋊Q8—2261no—
103C4×Q8—1132no—
104C4×Q8—2261no—
105#117—2261no—
106C2×C42—1131no—
107C4⋊C8—1131no—
108C4⋊C8—1131no—
109C4⋊C8—2261no—
110C4⋊C8—2261no—
111C4⋊C8C2×D11311yescharacteristic
112C4⋊C8C2×D11311yescharacteristic
113C2×Q8—21no—
114C2×Q8—1132no—
115C22×C4—1131no—
116C22×C4—1131no—
117C22×C4—1131no—
118M16—4522no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—4522no—
122C2×C8—2261no—
123C2×C8—2261no—
124C4⋊C4—21no—
125C4⋊C4—2262no—
126C4⋊C4—2262no—
127C4⋊C4—2261no—
128C4⋊C4—2261no—
129C4⋊C4C4×D11312yes—
130C22⋊C4—2262no—
131C42—1131no—
132C42—1131no—
133C42—1131no—
134C42—2262no—
135C42C22×D11311yescharacteristic
136C23—1131no—
137Q8—41no—
138Q8—41no—
139Q8—4522no—
140C2×C4—22no—
141C2×C4—1131no—
142C2×C4—1132no—
143C2×C4—1132no—
144C2×C4—1131no—
145C2×C4—1131no—
146C2×C4—4521no—
147C2×C4—2262no—
148C2×C4—2261no—
149C2×C4—2261no—
150C2×C4C2×C4×D11311yescharacteristic
151C2×C4D4×D11311yescharacteristic
152C2×C4D4×D11311yescharacteristic
153C8—41no—
154C8—41no—
155C8—4521no—
156C8—4521no—
157C22—1132no—
158C22—2261no—
159C22—2261no—
160C22C22⋊C4×D11311yescharacteristic
161C4—21no—
162C4—42no—
163C4—1132no—
164C4—4522no—
165C4—2261no—
166C4—2261no—
167C4SD16×D11311yescharacteristic
168C4Q16×D11311yescharacteristic
169C4#1681364611yescharacteristic
170C4#1681365111yescharacteristic
171C2—2262no—
172C2#2029858111yescharacteristic
173C2#103×D11311yescharacteristic
174C2#2029859611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#332×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C22⋊C4
cosocleC42×C113C23
hypercenter#332D113
hypocenterC113#1550
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #20298346C2semidirect
5. #20298346C2semidirect
6. #20298344C2semidirect
7. #332×C113C2semidirect
88. C113#1550semidirect
95. #332D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202991532
#202986202
C4⋊C8×D1132
#202983462
#202983442
#332×C1132
#1550113